Esperanza Lopez

Quantum corrections to the string Bethe ansatz

One-loop corrections to the energy of semiclassical rotating strings contain both analytic and non-analytic terms in the ’t Hooft coupling. Analytic contributions agree with the prediction from the string Bethe ansatz based on the classical S-matrix, but in order to include non-analytic contributions quantum corrections are required. We find a general expression for the first quantum correction to the string Bethe ansatz.One-loop corrections to the energy of semiclassical rotating strings contain both analytic and non-analytic terms in the t Hooft coupling. Analytic contributions agree with the prediction from the string Bethe ansatz based on the classical S-matrix, but in order to include non-analytic contributions quantum corrections are required. We find a general expression for the first quantum correction to the string Bethe ansatz.

The SU(3) spin chain sigma model and string theory

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N = 4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS5 × S 5 . The energy and spectrum of fluctuations for rotating circular strings with angular momenta along three orthogonal directions of the five-sphere is reproduced as a particular case from the spin chain sigma model.

Evolution of two-point functions from holography

A bstractWe consider a thermalization process in a 2-dimensional CFT that has a holographic description in terms of the gravitational collapse of a thin shell of null dust. This model represents a sudden perturbation of the CFT vacuum that communicates a uniform energy density to the system. We study the evolution of two-point functions at spacelike separated points (t1, l) and (t2, 0), and reproduce the generic pattern first derived from the analysis of quantum quenches to critical systems. A crucial characteristic of these setups is that the excitations generated by the initial perturbation presents non-trivial quantum correlations. As a consequence, for any ti< ∞ equilibration is only effective on finite regions whose size grows as a lightfront. The behavior on larger regions is greatly determined by the initial state, which for the quenches we consider and the holographic model has relevant differences. However in both cases for late times the dependence on the scale l of the two-point functions enters through the effective distance l − t1 − t2. We interpret the onset of this behavior as an equilibration time for occupation numbers in these 2-dimensional models.

UV/IR mixing via closed strings and tachyonic instabilities

We discuss UV/IR mixing effects in non-supersymmetric non- commutative U(N) gauge theories. We show that the singular (nonplanar) terms in the 2- and 3-point functions, namely the poles and the logarithms, can be obtained from a manifestly gauge invariant effective action. The action, which involves open Wilson line operators, can be derived from closed strings exchange between two stacks of Dbranes. Our concrete example is type 0B string theory and the field theory that lives on a collection of N electric D3-branes. We show that one of the closed string modes that couple to the field theory operator which is responsible for the infrared poles, is the type 0 tachyon.

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

N = 4 supersymmetric Yang-Mills operators carrying large charges are dual to semi- classical strings in AdS5 × S 5 . The spectrum of anomalous dimensions of very large oper- ators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

Spin chain sigma models with fermions

The complete one-loop planar dilatation operator of N = 4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2 , 2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N = 4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS 5 × S 5 with large angular momentum along the five-sphere.

Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions

We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational θ, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous N × N symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.

Closed strings tachyons and non-commutative instabilities

We observe a relation between closed strings tachyons and one-loop instabili- ties in non-supersymmetric non-commutative gauge theories. In particular we analyze the spectra of type-IIB string theory on C 3 =ZN orbifold singularities and the non-commutative fleld theory that lives on D3 branes located at the singularity. We flnd a surprising corre- spondence between the existence or not of one-loop low-momentum instabilities in the non- commutative fleld theory and the existence or not of tachyons in the closed string twisted sectors. Moreover, the relevant piece of the non-commutative fleld theory efiective action is suggestive of an exchange of closed string modes. This suggests that non-commutative fleld theories retain some information about the dynamics of the underlying string con- flguration. Finally, we also comment on a possible relation between closed string tachyon condensation and fleld theory tachyon condensation.

Holographic relaxation of finite size isolated quantum systems

A bstractWe study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2u2009+u20091 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically, an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the travelling shell is brought in correspondence with the evolution of the pattern of entanglement in the dual field theory. We propose, thereafter, that the observed oscillations are the dual counterpart of the quantum revivals studied in the literature. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.

Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism

We discuss nonplanar anomalies in noncommutative gauge theories. In particular we show that a nonplanar anomaly exists when the external noncommutative momentum is zero and that it leads to a non-conservation of the associated axial charge. In the case of nonplanar local anomalies, a cancellation of the anomaly can be achieved by a Green-Schwarz mechanism. In an example of D3 branes placed on an orbifold singularity that leads to a chiral theory, the mechanism involves twisted RR fields which propagate with zero noncommutative momentum. Global anomalies are not cancelled and, in particular, the decay � 0 → 2 is allowed.